First of all, I suggest being fairly knowledgeable in the workings of the company you're interested in. I LOVE manga and I try to keep myself fairly up to date on releases and announcements within the manga industry (I don't really enjoy anime as much, so my anime-related news is usually lacking).
Anime News Network http://www.animenewsnetwork.com is a pretty good resource, as is subscribing to their newsletters (most companies have them.)
I also found it useful to know what their products are, especially the ones that have either been newly released or are not the super popular series that EVERYONE knows about. Do your research and read a wide variety of their products. Devout fans are often the most passionate about the series that don't get enough love, and all the editors are fans, trust me.
Second, I would look around the corporate portions of the site to see if there is anything promising. I heard about the Viz internship from a friend who had done an internship with them herself